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In the original mDP protocol once all $z$ values received from each participant the following calculation is being done:

If either $XOR(z_1,z_2,...,z_n) = 0 $ or received invalid Signature then abort the the key computation. Else $z'_{j,j+1} = XOR(z'_{j_j-1},z'_{j})$

And the final Key will be: $k_i=H_g(z'_{1,2},\ldots,z'_{n,1},sid_i)$

But on the approach used (N+1)sec of the algorithm above the check $XOR(z_1,z_2,...,z_n) = 0$ is not performed thus I want to ask why in (N+1)sec this check is omitted?

Also I attempted to implement the key agreement, thus I want to ask in what conditions/requirements do I need so I can omit the check $XOR(z_1,z_2,...,z_n) = 0$ as well?

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